Worgan married three times over his lifetime. He married, firstly, Sarah Mackelcan at St Peter le Poer, London, in 1753. He had nine children with his wife; among whom was George Bouchier Worgan (bapt. 3 May 1757 at St Andrew's Church, Holborn), who was the naval surgeon on board the H.M.S. Sirius in the First Fleet to Australia, and Charlotte Sophia Worgan (bapt. 2 September 1761 at St Andrew's, Holborn) who married (at St Mary's church, Marylebone, in 1778) (Sir) Charles Parsons (d. 1817), later Master of the King's Band. Worgan obtained an Act of Parliament (9 Geo III c.57) in 1769 to divorce his wife for her adultery. He married, secondly, Eleanor Baston in 1770 (at St Andrew's, Holborn). He had two more children with Eleanor, the elder of whom was Thomas Danvers Worgan, subsequently a musicologist. He married, thirdly, Martha Cooke, a widow, in 1779 at St Mary, Aldermanbury.

John Worgan died at age 66 at Gower Street on 24 August 1790[3] after "an operation for the stone."[3] He was buried at St. Andrew Undershaft on 31 August. One of his favourite pupils, Charles Wesley[3] (1757–1834), presided at the organ.

A grandson, George Worgan (bapt. 18 January 1803 at St James's church, Chipping Campden, died 2 Apr 1888 at Tinakori Road, Wellington, New Zealand), was a musician of sufficient calibre to warrant a notice in the Musical Times upon his death.[4] George was an organist and pianoforte teacher, with a roster of students that included musicians' children and English nobility.[4] After retiring around 1850, he emigrated to New Zealand, where he raised sheep and taught music until his death at age 86.[4]

John Worgan's compositions include two oratorios: ‘Hannah’ (King's Theatre, Haymarket, 3 April 1, 1764) and 'Manasseh' (Lock Hospital Chapel, 30 April 1766); 'We will rejoice in Thy salvation,' a thanksgiving anthem for victories (29 Nov 1759); many songs for Vauxhall Gardens, of which thirteen books (at least) were published; psalm tunes, glees, organ music, and sonatas and other pieces for the harpsichord. Some of his manuscripts are in British Museum Addit. MSS. 31670, 31693, 34609, and 35038.

Richard Cecil wrote: "Admiration and feeling are very distinct from each other. Some music and oratory enchant and astonish, but they speak not to the heart... Dr. Worgan has so touched the organ at St. John's that I have been turning backward and forward over the prayer-book for the first lesson in Isaiah and wondered that I could not find Isaiah there!".[9]

Martin Madan, in a satirical song upon Joah Bates, issued anonymously, and set to music by Samuel Wesley, entitled 'The Organ laid open, &c.,' placed him as a player upon an equality with Handel: "Let Handel or Worgan go thresh at the organ".

Burney refers to him as "a very masterly and learned fugueist on the organ."[6]

^ abcdef"John Worgan". The Georgian Era: Memoires of the Most Eminent Persons, Who Have Flourished in Great Britain, from the Ascension of George the First to the Demise of George the Fourth, in Four Volumes. 4: Political and Rural Economists; Painters, Sculptors, Architects, and Engravers; Composers; Vocal, Instrumental, and Dramatic Performers. London: Vizetelly, Branston and Co. 1834. pp. 314–315.